Sideshow attractions bring to mind bearded-ladies and two-headed things, not babies like mine, that were born small and needed time in special incubators. In the early 1900's before hospitals has the technology to care for small and premature babies, they would often just tell parents, sorry, there's nothing that can be done. However, there was a man who had invented incubators for small babies, that the hospitals had denied would help. This man, named Dr. Martin A. Couney, offered those parents and those babies an option for life. He put tiny babies on display at Coney Island as part of an attraction and charged a 25 cent admission. This was how he paid for his services. He saved thousands. Such a fantastic story. Read more here and here.

Wikipedia describes Martin A. Couney this way:

Martin A. Couney was a physician and pioneer in neonatology. A student of Pierre-Constant Budin, he is best known for helping parents of premature infants by placing them in incubators when such technology was not allowed in most hospitals.[2][3] The incubators containing premature infants were on display at Coney Island, New York, where he charged 25 cents to view the children so parents would not have to pay for the child's medical care.[1][4] His exhibition at Luna Park opened in 1903.[5] Incubators were included in hospitals shortly before his death in 1950.[2][6]